How will the volume of the prism change if each side is increased by a factor of 4?

the new volume of the prism is times the original volume

Step-by-step explanation:

we know that

If two figures are similar, then the scale factor elevated to the cube is equal to the ratio of its volumes

Let

z------> the scale factor

x------> the volume of the dilated prism

y------> the volume of the original prism

so

In this problem we have

substitute

that means-----> the new volume of the prism is times the original volume

cheater

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b